You generated different ball then I was expecting... It's not based on truncated icosahedron... I tried to get 3DSOLID, but some lines aren't touching exactly with each others and beside all this, to make 3DSOLID those lines have to make exact planar polygons - sorry it was close - my routine recognized some polygons and converted them to regions, but major of them were not processed, so final surfsculpt was not good...

Well it's almost the same as your first example... I would say 12 regular pentagons and 80 irregular hexagons... I guess I counted wrong - thought 60 hexagons... But the same - no success in converting 3d lines to 3d solid... Only pentagons were good, but then again I think that not all were processed - not even single hexagon is good - you have to check their planar characteristics... Still not perfect...

Look I've counted your last example - it seems 12 regular pentagons and 110 irregular hexagons... I'll attach my counted version - you can check if you want...To answer your question : there are lisps for geodesic spheres and also there are lisps for all kind of dense covered spheres with regular triangles, quads, pentagons and hexagons based on uniform polyhedrons...M.R.

Here is my version of the same ball - 12 pentagons + 110 hexagons... I constructed based on dodecahedron - the problem still exist - we don't know ratio : edge of pentagon/hexagon : radius of sphere... I almost did it visually, but then the problem occurred when 2 cups had to be connected (bottom and top cup)... It seems that edge of pentagon should be little bigger, but we don't know how to determine that accurately...

Regards, M.R.

[EDIT : DWG removed due to lack of interest - not even single download up to now... See date of edit below post...]